This smells like Homework, but since you are asking for guidance - here is some.

You need to analyze the problem, and come up with a data structure that will allow you to verify no duplicates.

To simplify the data structure, you could flatten out Courses and grades , and map it to something like this:

[Math A+] [Math A] [Math B+] ..... [Math F-]
 Stu1              Stu2     ....    Stu3


[Gov A+] ......                  ..[Gov F-]
Stu5       Stu3         ....
[download]

This maps to one Single-dimensional Array per subject. Of course, there are many ways to do this. Hope this helps.